Polynomials

Question

form a polynomial whose zeros are -3,3,9 with the degree of 3

Answer 1

By Factor Theorem, if x = a is a zero of f(x), then  (x - a) is a factor of f(x).

 

Therefore, (x - 3), (x + 3), and (x - 9) are factors of the polynomial, f(x), that needs to be formed.

 

   f(x) = a (x -3) (x + 3) (x - 9) where a is real.

 

Note there is an infinite number of polynomials with the given zeros. One such polynomial is where a = 1.

 

  f(x) = (x² - 9) (x - 9)

 

 f(x) = x³ - 9x² - 9x + 81